CS 782: An Introduction to
Geometric Complexity Theory.
The course aims to introduce Geometric Complexity Theory
(GCT),
a particular approach to understanding computational
complexity, along with the algebraic and geometric tools
needed. The basic preparation which is required as a
prerequisite is basic group theory, linear alegbra and
commutative algebra and some rudimentary notions of ideals
and varieties. Most of this will be reviewed through
examples which lie on the GCT path.
We will use some standard books: Humphreys, for
Algebraic Groups, Harris for Algebraic Geometry and others
as and when needed. These are NOT prerequisites. We will
also be reading research papers.
The class will meet twice a week, for the initial few weeks.
Familiarity required: Linear Algebra, Basic Algebra,
Commutative algebra, Groups
and group actions, group representation, ideals and varieties. Artin's Algebra is adequate.
Detailed Course contents pdf
Lecture topics and notes pdf
Some reference books:
Kunze, Algebraic Geometry and Commutative Algebra pdf
Sturmfels, Algorithms in Invariant Theory pdf
Humphreys, Algebraic Groups pdf
Harris, Algebraic Geometry pdf
Derksen, Constructive Invariant Theory pdf